D9.C.5 Member Capacities
D9.C.5.1 Design Capabilities
All types of available shapes such as HShape, IShape, LShapes, channel, pipe, tube, etc. can be used as member property and STAAD.Pro will automatically adopt the design procedure for that particular shape if Steel Design is requested. The steel tables available within STAAD.Pro or user provided table (UPTABLE) can be used for member properties.
D9.C.5.2 Methodology
For steel design, STAAD.Pro compares the actual stresses with the allowable stresses as required by AIJ specifications. The design procedure consist of following three steps.
Calculation of sectional properties
The program extracts section properties cross sectional area, A, the moment of inertia about Y and Z axes, I_{yy} and I_{zz}, and the St. Venant torsional constant, J, from the builtin steel tables. The program then calculates the elastic section moduli, Z_{z} and Z_{y}, torsional section modulus, Z_{x}, and radii of gyration, i_{y} and i_{z}, using the appropriate formulas.For I shapes, H shapes, and channel sections, the program calculates the radius of gyration needed for bending using following formula:
$i=\sqrt{{I}_{i}/{A}_{i}}$
Calculation of actual and allowable stresses
Allowable stresses for structural steel under permanent loading shall be determined on the basis of the values of F given in the following table.
Table 1. Table: Values of F (N/mm^{2}) Steel for Construction Structures Steel for General Structures Steel for Welded Structures Thickness SN400 SNR400
STKN400
SN490 SNR490
STKN490
SS400 STK400
STKR400
SSC400
SWH400
SS490 SS540 SM400 SMA400
SM490 SM490 Y
SMA490
STKR490
STK490
SM520 SM570 t≤ 40 235 325 235 275 375 235 325 355 400 40< t ≤ 100 215 295 215 255  215 295* 335 400 * F = 325 N/mm^{2} when t > 75mm
Note: In checking members for temporary loading be the combination of stresses described in Chap.3, allowable stresses specified in this chapter may be increases by 50%Program calculates actual and allowable stresses by following methods:

Axial Stress:
Actual tensile stresses,
whereF_{T} = force / ( A × NSF )  NSF
=  Net Section Factor for tension input as a design parameter
Actual compressive stress , F_{C} = force / A
Allowable tensile stress, f_{t}
 = FYLD / 1.5 (For Permanent Case)
 = FYLD ( For Temporary Case )
 FYLD
=  Yield stress input as a design parameter
Allowable compressive stress, f_{c}
${f}_{c}=\{\begin{array}{c}\frac{[10.4{\left(\frac{\lambda}{\Lambda}\right)}^{2}]F}{\nu}\phantom{\rule{0ex}{0ex}}\text{when}\phantom{\rule{0ex}{0ex}}\lambda \le \Lambda \\ \frac{\begin{array}{c}0.277F\end{array}}{{\left(\frac{\lambda}{\Lambda}\right)}^{2}}\phantom{\rule{0ex}{0ex}}\text{when}\phantom{\rule{0ex}{0ex}}\lambda >\Lambda \end{array}$
where= f_{c} × 1.5 (for Temporary case)  Λ
=  $\sqrt{\frac{{\pi}^{2}E}{0.6F}}$
 ν
=  $\frac{3}{2}+\frac{2}{3}{\left(\frac{\lambda}{\Lambda}\right)}^{2}$
Actual torsional stress, f_{t} = torsion / Z_{x}
where Z_{x}
=  J / max(t_{f}, t_{w})
 t_{f}
=  flange thickness
 t_{w}
=  web thickness

Bending Stress:
Actual bending stress for My for compression
( F_{bcy}) = M_{y} / Z_{cy} Actual bending stress for Mz for compression
( F_{bcz}) = M_{z} / Z_{cz} Actual bending stress for My for tension
( F_{bty} ) = M_{y} / Z_{ty} Actual bending stress for Mz for tension
where( F_{btz} ) = M_{z} / Z_{tz}  Z_{cy}, Z_{cz}
=  elastic section modulus for compression due to bending about the y and z axes, respectively
 Z_{ty}, Z_{tz}
=  elastic section modulus for tension due to bending about the y and z axes, respectively
Note: The web is ignored in the calculation of Z_{z} for Hshape, Ishape, and channel sections when the MBG parameter = 1.Allowable bending stress for M_{y}
(f_{bcy}) = f_{t}
Allowable bending stress for M_{z}
(f_{bcz}) = { 1  .4 x (lb / i)^{2} / (C λ^{2})} ft max = 89,000/ (lb × h / A_{f} ) For Temporary case, f_{bcz} = 1.5 x (f_{bcz} for Permanent case)
where C
=  1.75  1.05 (M2 / M1) + 0.3 (M2 / M1)^{2}
 Allowable bending stress for M_{y}, f_{bty} = f_{t}
 Allowable bending stress for M_{z}, f_{btz} = f_{bcz}

Shear Stress
Actual shear stresses are calculated by the following formula:
whereq_{y} = Q_{y} / A_{ww}  A_{ww}
=  web shear area = product of depth and web thickness
whereq_{z} = Q_{z} / A_{ff}  A_{ff}
=  flange shear area = 2/3 times total flange area
 f_{s}
=  Allowable shear stress, F_{s} / 1.5, F_{s} = F / √(3)


Checking design requirements:
User provided RATIO value (default 1.0) is used for checking design requirements
The following conditions are checked to meet the AIJ specifications. For all the conditions calculated value should not be more than the value of RATIO. If for any condition value exceeds RATIO, the program gives the message that the section fails.
Conditions:
 Axial tensile stress ratio = F_{T} / f_{t}
 Axial compressive stress ratio = F_{C} / f_{c}
 Combined compression & bending compressive ratio = F_{C} / f_{c}+F_{bcz}/f_{bcz}+F_{bcy}/f_{bcy}
 Combined compression & bending tensile ratio = (F_{btz}+F_{bty}F_{C}) / f_{t}
 Combined tension & bending tensile ratio = (F_{T}+F_{btz}+F_{bty}) / f_{t}
 Combined tension & bending compressive ratio = F_{bcz}/f_{bcz}+F_{bcy}/f_{bcy} F_{T}/f_{t}
 Shear stress ratio in Y = q_{y} / f_{s}
 Shear stress ratio in Z = q_{z} / f_{s}
 von Mises stress ratio (if the von Mises stresses were set to be checked) = f_{m}/(k⋅f_{t})
D9.C.5.4 Allowable stress for Axial Tension
Allowable axial stress in tension is calculated per section 5.1 (1) of the AIJ code. In members with axial tension, the tensile load must not exceed the tension capacity of the member. The tension capacity of the member is calculated on the basis of the member area. STAAD calculates the tension capacity of a given member based on a user supplied net section factor (NSFa default value of 1.0 is present but may be altered by changing the input value, see Table 8B.1) and proceeds with member selection or code checking.
D9.C.5.5 Allowable stress for Axial Compression
The allowable stress for members in compression is determined according to the procedure of section 5.1 (3). Compressive resistance is a function of the slenderness of the crosssection (Kl/r ratio) and the user may control the slenderness value by modifying parameters such as KY, LY, KZ and LZ. In the absence of user provided values for effective length, the actual member length will be used. The slenderness ratios are checked against the permissible values specified in Chapter 11 of the AIJ code.
D9.C.5.6 Allowable stress for Bending
The permissible bending compressive and tensile stresses are dependent on such factors as length of outstanding legs, thickness of flanges, unsupported length of the compression flange (UNL, defaults to member length) etc. The allowable stresses in bending (compressive and tensile) are calculated as per the criteria of Clause 5.1 (4) of the code.